Hitch Locks can be two edged sword. If you lose the key for some you could be in big trouble. For that reason we keep a spare key hidden inside our trailer. I'd tell you where we hide it, but then I'd have to order yet another hit and I have already used up this months pre-paid allowance.
Latch locks can usually be bypassed simply by disassembling and reassembling the hitch.
We have a Fulton Gorilla Guard on our Lil' BigFoot
, and it's fine for our home parking space and at campgrounds. However, I think that it can be easily defeated with brute force and would not suggest using one in a storage area where you might not see your trailer for weeks or months at a time.
BTW: Most storage facilities offer little or no insurance against theft or damage to your trailer when parked therein. Be sure to ask them and your ins company.